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Theorems · Theorem · real analysis

HasStrictFDerivAt.csin

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : E → ℂ} {f' : StrongDual ℂ E} {x : E},
  HasStrictFDerivAt f f' x → HasStrictFDerivAt (fun x => Complex.sin (f x)) (Complex.cos (f x) • f') x
Defined in
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
Cited by
0 results in Mathlib
Foundations
Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpace
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RingHom.id · cited by 18349RingHom.idNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceComplex · cited by 5565ComplexStrongDual · cited by 459StrongDualComplex.cos · cited by 279Complex.cosHasStrictFDerivAt · cited by 261HasStrictFDerivAtComplex.sin · cited by 258Complex.sinHasStrictDerivAt.comp_hasStrictFDerivAt · cited by 19HasStrictDerivAt.comp_has…Complex.hasStrictDerivAt_sin · cited by 5Complex.hasStrictDerivAt_…HasStrictFDerivAt.csinCITED BYCITES

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